microeconomics3070profbarham-預(yù)覽頁
【正文】 mize or minimize). 2. Constraint: limits or restrictions that are imposed on the decision maker Constrained Optimization Examples You want to maximize your happiness during your second year at CU. ? Objective function Utility (happiness): Utility=f(days skied per month (s), beers per week(b)). U=s*b ? The thing you are maximizing or minimizing ? Constraints: . (subject to) Ine (I)=S*Ps+B*Pb, where P is price ? Many max or min problems have some kind of a constraint you have to work with Writing Out Statement of Constrained Optimization Problem M A Xs , bU = s * bs . t I = s * P s + b * P bObjective Function Endogenous Variables Constraint Marginal Analysis ? Solution to a constrained optimization problem depends on the marginal impact of the decision variables on the value of the objective function. But what is marginal? ? The term marginal tells us how the value of the objective function changes as a result of adding one unit of a decision variable. Marginal Analysis Happiness $ spent From beer From skiing 0 0 0 25 80 4 50 90 10 75 92 15 100 94 20 Marginal Happiness From beer From skiing 80 4 10 6 2 5 2 5 How much do you spend on beer and skiing to Maximize your happiness if you have 100 budget? Marginal Analysis ? $100 on beer = 94 units of happiness ? $75 beer plus $25 skiing = 96 units of happiness. ? $50 on beer and $50 on skiing = 100 units of happiness. ? Yes a day of skiing with a nice apres ski makes you very happy. Marginal Analysis You just did a constrained optimization problem ? Optimize happiness (beer and skiing) subject to $100 weekly entertainment budget. H(b, s) . Ps*s + Pb*b=100 where b= quantity of bee
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